The deadliest attack took place in Baghdad's Shiite northern Shaab neighbourhood, when two parked car bombs exploded simultaneously near a restaurant and a tea house.
Officials say those blasts killed 10 people and wounded 26.
Authorities said that a parked car bomb ripped through in capital's Shiite eastern district of Sadr City, killing five and wounding 10. Another bombing killed three civilians and wounded six in a commercial area in the central Bab al-Muadham neighbourhood, officials said. Two other bombings killed two civilians and wounded 13, police said.
The attacks come as Iraqi security forces are besieging two key cities country's western Anbar province after they were taken over by militants from al-Qaida's local branch, known as the Islamic State in Iraq and Levant. Clashes have been taking place since Monday in Anbar's provincial capital, Ramadi, and nearby Fallujah between al-Qaida militants and pro-government Sunni tribesmen. The Baghdad bombings could be seen as an attempt by militants to distract security forces.
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Earlier today, a senior Iraqi military commander said that it will take a few days to fully dislodge al-Qaida-linked fighters from two key western cities.
"The quiet and safe life that is sought by the Anbaris will not be completely restored before few hours or two to three days, God willing," Fleih said.
Residents say it has been quiet since yesterday night in Fallujah, where militants still control the centre of the city. Sporadic clashes took place today in and around Ramadi. The residents spoke on condition of anonymity for their safety.
ISIL is also one of the strongest rebel units in Syria, where it has imposed a strict version of Islamic law in territories it holds and kidnapped and killed anyone it deems critical of its rule.